Green’s Dictionary of Slang

a nickname for either a very tall or a very short man.

1916		C.J. Dennis ‘The Push’ in Moods of Ginger Mick 40: Then there’s Lofty Craig uv Queensland, ’oo’s a special pal uv mine; / Slow an’ shy, an’ kind o’ nervous uv ’is height.
1922		‘J.H. Ross’ Mint (1955) 96: Lofty, our six-foot-two weed of a naval telegraphist, unfolded himself from the bed.
1928		Age (Melbourne) 10 Nov. 23/2: ‘Stone the crows! If it isn’t Lofty Anderson’.
1939		V. Davis Gentlemen of the Broad Arrows 222: Warder ‘Lofty H—’ 6 feet 6 inches in height, stood [...] near the sentry-box.
1941		G. Casey ‘Short Shift Saturday’ in Mann Coast to Coast 207: Lofty was only kidding them along.
1950		A. Buckeridge Jennings Goes To School 130: ‘Can’t see any fire,’ said Lofty.
1968		D. O’Grady A Bottle of Sandwiches 117: ‘Lofty’s the name,’ he said offering a paw the size of a large dinner plate.
1977		(con. 1941) R. Beilby Gunner 166: Lofty was smoking a powdery smelling Greek cigarette.